# 15 21 23 triangle

### Acute scalene triangle.

Sides: a = 15   b = 21   c = 23

Area: T = 153.7310893122
Perimeter: p = 59
Semiperimeter: s = 29.5

Angle ∠ A = α = 39.53662915601° = 39°32'11″ = 0.69900384618 rad
Angle ∠ B = β = 63.0243617313° = 63°1'25″ = 1.10999696286 rad
Angle ∠ C = γ = 77.44400911269° = 77°26'24″ = 1.35215845632 rad

Height: ha = 20.49774524162
Height: hb = 14.64110374402
Height: hc = 13.36879037497

Median: ma = 20.70662792408
Median: mb = 16.33224829711
Median: mc = 14.16986273153

Inradius: r = 5.2111216716
Circumradius: R = 11.78219519761

Vertex coordinates: A[23; 0] B[0; 0] C[6.80443478261; 13.36879037497]
Centroid: CG[9.93547826087; 4.45659679166]
Coordinates of the circumscribed circle: U[11.5; 2.5622107017]
Coordinates of the inscribed circle: I[8.5; 5.2111216716]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 140.464370844° = 140°27'49″ = 0.69900384618 rad
∠ B' = β' = 116.9766382687° = 116°58'35″ = 1.10999696286 rad
∠ C' = γ' = 102.5659908873° = 102°33'36″ = 1.35215845632 rad

# How did we calculate this triangle?

Now we know the lengths of all three sides of the triangle and the triangle is uniquely determined. Next we calculate another its characteristics - same procedure as calculation of the triangle from the known three sides SSS. ### 1. The triangle circumference is the sum of the lengths of its three sides ### 2. Semiperimeter of the triangle ### 3. The triangle area using Heron's formula ### 4. Calculate the heights of the triangle from its area. ### 5. Calculation of the inner angles of the triangle using a Law of Cosines    